With hard disks of higher density and larger capacity, the distance between a magnetic disk and a header becomes shorter, thereby requesting slider design with a smaller deviation of fly-height that would be caused by an elevation difference or a disk radial position.
As illustrated in FIG. 15 as a component assigned a reference numeral 1501, a slider is provided at the back of the tip of an actuator 1502 moving on a magnetic disk in a hard disk drive, and the position of the header is calculated by the shape of the slider 1501.
When the optimal shape of the slider 1501 is determined, the efficient calculation of so-called multiobjective optimization for simultaneously minimizing the functions relating to a fly-height (1503 in FIG. 15) that is associated with the position of the header, to a roll (1504) and to a pitch (1505) is to be performed.
More generally speaking, in a designing stage in manufacture, it is necessary to represent a design condition as one or more functions, that is, objective functions, relating to a design parameter (or design parameters), and to set a design parameter (or design parameters) for minimizing the objective functions, that is, to perform the optimization.
Conventionally performed is not directly solving a multiobjective optimization problem, but realizing single objective optimization by obtaining the minimum value of a linear sum f of terms, each of which is obtained by multiplying each objective function fj by a weight kj as represented by the following equation (1).f=k1·f1+k2·f2+ . . . +kt·ft  (1)
After a designer determines the basic shape, the respective domains of parameters p, q, r, etc. to define the slider shape S illustrated in FIG. 16 are set by a program. The function f is calculated over and over with the values of the parameters p, q, r, etc. gradually changed so that the slider shape can be calculated to minimize the function value f.
The function f depends on the weight vector K=(k1, k2, . . . , kt). In the practical design, the minimum value of the function f with respect to each changed value is calculated while further changing the weight vector K. Then, by totally determining the balance between the calculated minimum value of the function f and the weight vector K, the slider shape is determined.
As described above, since there is a trade-off between functions in the multiobjective optimization including a plurality of objective functions, the number of calculated optimal solutions is not limited to one.
For example, if the optimization on the first objective function value is performed for “reducing a weight” as well as the optimization on the second objective function value is performed for “reducing a cost” in designing a product, the values of the first objective function and the second objective function can be various coordinate values in the two-dimensional coordinate system as illustrated in FIG. 17 depending on the manner of assigning a design parameter (or design parameters).
Since it is required that the values of both first objective function and the second objective function are small (namely, light weight and low cost is required), the points on a line 1703 connecting calculated points 1701-1, 1701-2, 1701-3, 1701-4, or 1701-5 in FIG. 17 and the points close to the line 1703 can be a group of optimal solutions.
As exemplified above, when there are a plurality of conditions such as the first objective function and the second objective function, the solution that can be a value satisfying an objective, at a higher level than another value does, in all objective functions and that can also be an apparently good value in one or more objectives is called a Pareto optimal solution or a non-dominated solution, and the boundary illustrated as the line 1703 in FIG. 17 is called a Pareto boundary. All non-dominated solutions can also be called solutions of multiobjective optimization.
In the calculated points 1701-1 through 1701-5 in FIG. 17, the calculated point 1701-1 corresponds to a model that costs high but can be light in weight, and the calculated point 1701-5 corresponds to a model that is not light in weight but costs low.
On the other hand, since the calculated points 1702-1 and 1702-2 are points corresponding to models that can be lighter in weight or cost lower, they cannot be optimal solutions. They are called dominated solutions.
Thus, in the multiobjective optimizing process, it is very important to be able to appropriately grasp non-dominated solutions (i.e., Pareto optimal solutions). To attain this, it is important to efficiently calculate non-dominated solutions for desired objective functions.    [Patent Document 1] Japanese Laid-open Patent Publication No. 07-44611